Hard problems for simple default logics
Artificial Intelligence - Special issue on knowledge representation
The complexity of logic-based abduction
Journal of the ACM (JACM)
Semantics and complexity of abduction from default theories
Artificial Intelligence
LOF: identifying density-based local outliers
SIGMOD '00 Proceedings of the 2000 ACM SIGMOD international conference on Management of data
Yet some more complexity results for default logic
Artificial Intelligence
Algorithms for Mining Distance-Based Outliers in Large Datasets
VLDB '98 Proceedings of the 24rd International Conference on Very Large Data Bases
Editorial: special issue on learning from imbalanced data sets
ACM SIGKDD Explorations Newsletter - Special issue on learning from imbalanced datasets
A Survey of Outlier Detection Methodologies
Artificial Intelligence Review
Outlier detection by logic programming
ACM Transactions on Computational Logic (TOCL)
Outlier detection using default reasoning
Artificial Intelligence
DOLPHIN: An efficient algorithm for mining distance-based outliers in very large datasets
ACM Transactions on Knowledge Discovery from Data (TKDD)
ACM Computing Surveys (CSUR)
Normality and faults in logic-based diagnosis
IJCAI'89 Proceedings of the 11th international joint conference on Artificial intelligence - Volume 2
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It was noted recently that the framework of default logics can be exploited for detecting outliers. Outliers are observations expressed by sets of literals that feature unexpected properties. These observations are not explicitly provided in input (as it happens with abduction) but, rather, they are hidden in the given knowledge base. Unfortunately, in the two related formalisms for specifying defaults - Reiter's default logic and extended disjunctive logic programs - the most general outlier detection problems turn out to lie at the third level of the polynomial hierarchy. In this note, we analyze the complexity of outlier detection for two very simple classes of default theories, namely NU and DNU, for which the entailment problem is solvable in polynomial time. We show that, for these classes, checking for the existence of an outlier is anyway intractable. This result contributes to further showing the inherent intractability of outlier detection in default reasoning.